Solskjaer, who is currently the manager of Norwegian champions Molde, has been linked with the vacant managerial role at Blackburn Rovers.
But dramatically shortened bookies odds puts him a close second to Mick McCarthy for the Bolton seat, which means attention could now switch from a move to Ewood Park to the Reebok Stadium instead.
Solskjaer has enjoyed an impressive start to his managerial career after he guided Molde to their first Norwegian league title last season.
He has since engineered another successful campaign for Molde, who are on the brink of defending their title. As well as success as Modle, Solskjaer also won the reserve league with Manchester United Reserves and he is proving a popular choice in The Bolton News' snap poll online.
But much hinges on his desire to leave Norway. He turned down the opportunity to manage Barclays Premier League side Aston Villa in the summer..
Current odds for Solskjaer, which were 7/1 this morning, are now 2/1 at Betfred, 7/2 at Ladbrokes and 9/2 at Coral. McCarthy is evens on some websites and remains the favourite.